Answer
There is no solution.
Work Step by Step
The absolute value of $x,$ written as $|x|,$ is the distance of $x$ from $0,$ and hence, is always a nonnegative number. Therefore, the left side of the given equation, $
|7x-2|=-9
,$ is always nonnegative. This is never equal to the expression at the right. Hence, $\text{
there is no solution
.}$